if \frac{b+c-a}{a}\:, \frac{c+a-b}{b}\: , \frac{a+b-c}{c}   are in A.P Then

which of the following in A.P

 

  • Option 1)

    a,b,c

  • Option 2)

    a^{2},b^{2},c^{2}

  • Option 3)

    \frac{1}{a},\frac{1}{b},\frac{1}{c}

  • Option 4)

    Non of these

 

Answers (1)

As learnt in concept

Properties of an A.P. -

If a fixed number is added to (Subtracted from) each term of a given A.P, then the resulting sequence is also an AP.

- wherein

If a_{1},a_{2},a_{3},--------- is an AP

then  a_{1}\pm K,a_{2}\pm K,a_{3}\pm K,---------

is also an AP

 

 

Properties of an A.P. -

If each term of an AP is multiplied by a fixed constant (or divided by a constant),then resultant is also an AP.

- wherein

If  a_{1},a_{2},a_{3}------is \: AP

Then Ka_{1},Ka_{2},Ka_{3}------is \: AP

and a_{1}/K,a_{2}/K,a_{3}/K------is \: also \: an \: AP

 

 \frac{b+c}{a}-1; \frac{c+a}{b}-1; \frac{a+b}{c}-1 are in AP

Add 2 to all the terms.

\frac{b+c+a}{a}, \frac{c+a+b}{b}, \frac{a+b+c}{c} are in AP

Divide by (a+b+c), we get

\frac{1}{a}, \frac{1}{b}, \frac{1}{c} are in AP


Option 1)

a,b,c

This solution is incorrect

Option 2)

a^{2},b^{2},c^{2}

This solution is incorrect

Option 3)

\frac{1}{a},\frac{1}{b},\frac{1}{c}

This solution is correct

Option 4)

Non of these

This solution is incorrect

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